Rupert Murdoch should be questioned by the public inquiry into the phone hacking scandal, David Cameron said yesterday.

The 80-year-old media mogul could be asked to give evidence under oath by Lord Justice Leveson, a senior judge, who will investigate the behaviour of newspapers and the police in the hacking affair and future press regulation.

Government lawyers believe Mr Murdoch would have to attend the inquiry if he were in the UK, which he normally visits a few times a year. However, he could not be stopped from leaving the country as soon as such a request were made – or, as an American citizen, be forced to return to this country from abroad. Ministers hope he will feel "moral pressure" to turn up.

More immediately, the chairman of News Corp must decide by 10am this morning whether to attend a hearing of the Commons Culture Media and Sport Committee next Tuesday, which believes it was misled over the scale of hacking by News International (NI) during its previous investigation. The committee has also invited his son James, News Corp's chief executive in Europe, and Rebekah Brooks, chief executive of NI.

Only Mrs Brooks, as a UK citizen, could be forced to attend. She may be summoned to the Bar of the Commons chamber if she refuses. The deadline for a response from all three was extended last night after signals from NI that it would respond positively.

Announcing the judicial inquiry, Mr Cameron said anyone guilty of wrongdoing – or sanctioning illegal practices – should be banned from running media organisations. The Prime Minister said the inquiry would "have the power to summon witnesses including newspaper reporters, management, proprietors, policemen and politicians of all parties to give evidence under oath and in public." Mr Cameron, Tony Blair and Gordon Brown are expected to be called to give evidence. The first part of two-pronged investigation will include the culture, practices and ethics of the press; the failure of the current system of newspaper regulation; the relationship between press and politicians and the issue of cross-media ownership.

Part two will look at the specific allegations of unlawful conduct by the News of the World; the original police inquiry into hacking and evidence of corrupt payments to police officers. Most of this phase will be delayed until after the current police investigation.

However, the two-stage process faces criticism on the grounds that the lessons drawn when specific allegations are investigated will not be available when general conclusions are drawn in part one.

Mr Cameron also announced plans to change the ministerial code to require ministers to "record all meetings with newspaper and other media proprietors, senior editors and executives – regardless of the nature of the meeting". This means that social as well as formal occasions would be registered. The new rule will also apply to permanent secretaries and special advisers.

Lord Leveson said: "The inquiry must balance the desire for a robustly free press with the rights of the individual while... ensuring that critical relationships between the press, Parliament, the Government and the police are maintained." He added: "The press provides an essential check on all aspects of public life. That is why any failure within the media affects all of us. At the heart of this inquiry, therefore, may be one simple question: who guards the guardians?" The terms of the inquiry were agreed by the three main party leaders after Ed Miliband and Nick Clegg used "back channels" to agree that it should be judge-led. Mr Cameron was seen as slower off the mark but backed the move.

Welcoming the terms of the inquiry, Mr Miliband said: "The revelations of the past week have shocked the whole country and the public now rightly expect those of us in this house – those who represent them – to provide not just an echo for that shock, but the leadership necessary to start putting things right."

Profile: Brian Leveson

Earlier this year The Sun labelled Lord Justice Brian Leveson "a softie" for his stance on sentencing criminals. They are words which may come back to haunt Rupert Murdoch's best-selling newspaper after the judge was yesterday unveiled as the head of the public inquiry into the ethics and practices of the press.

The 62-year-old barrister has wide experience of dealing with media in a career which saw him prosecute Rose West, Britain's most prolific female serial killer, and more recently led to his appointment as head of the Sentencing Council, which handles the political hot potato of recommending jail terms.

The Oxford-educated Court of Appeal judge, who is married with three children and lists walking as an interest, will be aided by a panel of experts but will need to steer a course through the legal, political and moral minefield of media regulation and press freedom.

Legal experts yesterday pointed out his reputation as a stickler for fair trials and due process with one QC describing him as a "steady pair of hands".

Sir Brian will be well aware of the ability of a media firestorm to derail a carefully-considered programme of reforms. The work of the Sentencing Council contributed to the new guidelines on the early release of prisoners, which were dropped by justice secretary Ken Clarke last month.

Cahal Milmo

Q&A

What will the inquiry announced by David Cameron cover?

Part one will cover "the culture, practices, and ethics of the press, including: contacts between national newspapers and politicians; the relationship between the press and the police; the extent to which the current policy and regulatory framework has failed; and the extent to which there was a failure to act on previous warnings about media misconduct."

What about the phone-hacking scandal?

Part two will – eventually — look into "the extent of unlawful or improper conduct within News International and other newspaper organisations"; the way the police investigated the initial allegations and the review by the Metropolitan Police of its first investigation; the extent to which the police received corrupt payments or were complicit in suppressing its proper investigation; and the corporate governance and management failures at News International and other newspaper organisations.

How long will it take?

Part one will start work shortly and should be completed within 12 months, David Cameron said yesterday. However, such inquiries often take much longer than expected. Most of part two will be delayed to avoid prejudicing any prosecutions arising from the police investigation into hacking and police corruption. That could take a very long time. The Met have to contact another 3,700 possible victims of hacking, and are currently doing so at the rate of 30 a month. So if the glacial rate of progress continues, everyone involved should know some time before 2021.

What is the most likely change to result from the inquiry?

An end to self-regulation of the press and the much-criticised Press Complaints Commission and its head, Baroness Buscombe. Some MPs favour statutory regulation – for example, writing the industry's code of conduct into law. But Mr Cameron, Nick Clegg and Ed Miliband are wary of any system that appears to allow politicians to control the press.

Andrew Grice

Britain's top public inquiries

Macpherson 1999 – death of Stephen Lawrence

In one of the most influential inquiries in recent decades, Lord Macpherson found that the Metropolitan Police was guilty of "institutional racism" in its response to the murder of the black teenager Stephen Lawrence in Eltham, south-east London, in 1993. Lasting 19 months and costing £4.2m, the inquiry heard evidence from the five young men suspected of the killing and has been described as a landmark in British criminal justice.

Saville 1998-2010 – Bloody Sunday

The longest and, at £195m, the most expensive public inquiry in British history. found that the shooting of 13 demonstrators in Londonderry in 1972 was unjustified, and heavily criticised the British Army. Critics said it had elevated the victims of the shooting to a higher status than that of other victims of the Troubles.

Hutton 2003 – death of David Kelly

The inquiry into the suicide of the government scientist David Kelly was criticised for failing to examine wider intelligence gathered in the run-up to the war in Iraq. Critics, including The Independent, described the report as a "whitewash". It was produced over six months at a cost of £1.7m.

Phillips 2000 – BSE

Lasting three years and costing £26m, Lord Phillips found that the crisis over the disease BSE in cattle was too complex and too prolonged to be pinned on a single individual or decision. The inquiry sought to learn lessons from the leap of BSE to a human disease, vCJD, which caused a crisis for British agriculture, tragedy and warnings of a timebomb forhuman health.

Cullen 2001 – Ladbroke Grove rail crash

The 270-page report into the 1999 rail crash that killed 31 and left more than 520 injured made 89 recommendations and called for an overhaul of rail safety. After sitting for 31 months at a cost of £8.6m, it found the prime cause of the crash was the driver of a Thames Trains service passing a red light.